Electrical delay network



H. NYQUIST ET AL 1,732,313v

ELECTRICAL DELAY NETWORK Oct. 22,- 1929.

Filed Sept. ll, 1926 2 Sheets-Sheet l Positgmo 4of Equdibf'zam/ C W4 TTORNEYS.

Oct. 22, 1929. H. NYQUlsT z-:T AL

ELECTRICAL DELAY NETWORK Filed Sept. ll, 1926 elay w seconds 2 Sheets-Sheet 2 Heacz'ance fmque/zcy -I- C7 I-C? T63 T64 fleet/'[0 Maw/'k Egaiualent to 2 no Y 2500 Weg/:fancy INVENTORS TORNEYS.

Patente-d @et 22, i929 COR-PORATON OF NEW YORK NT; FFICE EFLEGER, 0F ARLINGTON, NEW AND TELEGRAPH COMPANY, A.

ELECTRCAL DELAY NET'i/VORK Application filed September 11, 1925. Serial No. 134,929.

yThis invention relates to an electro-niechanical device and more particularly to a combined electrical and mechanical device in which the mechanical part is designed to simulate certain electrical circuits or parts of circuits.

In various electrical circuits, such as transmission lines, it has been found advantageous to introduce electrical apparatus, such as correcting networks to modify the characteristics of the line as a whole or artificial line networks to balance or to terminate a line. The precision with which a desired result, such as a simulation by a correcting network or an artificial line, may be obtained will in general depend en the number of degrees of freedom in the apparatus, and in the illustrations given, this refers to the number of elements of capacity, inductance or resistance present. In correcting` networks and artificial lines it has been convenient to build them of a series of sections of such elements, the greater the number of sections used the greater the degree of simulation possible. ln some cases, the cost places a sharp prohibition to the use of these networks or limits the number of sections which is feasible. Various attempts have been made, with some success, to devise simplified and composite circuits which will be more economical but this has only partially solved the problem. ln this invention, we provide for substituting mechanical devices, in whole or in part, for electrical circuits or parts thereof.

An objectof the invention, then, is to devise a mechanical means, properly associated with the electric lines or circuits, which shall serve as the equivalent of electrical networks. A. further object is to develop design formul by which a mechanical. device may be constructed to simulate a particular electrical network or to exhibit electrical characteristics on a quantitative basis.

The invention. will be better understood by reference to the following specification and accompanying drawing in which Figure l represents a simple form of electro-mechanical device whereby electrical reactance may be obtained by mechanical means; Fig. 2 shows another and preferred means for this purpose; Figs. 3 to 6 show parts of electric circuits to be simulated; Figs. 7 and 8 are diagrams used in explaining the operation of the invention; Fig. 9 is a curve showing various relations necessary for our method of design and Fig. l() shows a circuit which is the equivalent of the device of Fig. 2.

In the following analysis of the combined electrical and mechanical device it has been found convenient to make use of certain analogies which exist between electrical systems and mechanical systems thus simplifying the necessary equations. rlhese analogies are not merely qualitative but quantitative and identical, and the same symbols will be used. rl`he corresponding quantities in the two systems, which we will encounter, are:

Electrical system Mechanical system Charge Displacement Current Velocity of mass Electromotive force Force lnductance Mass Capacity Reciprocal of stiffness or elasticity Resistance Friction Referring more particularly to Fig. 1, we shall now prove that for the simple mechanical device as shown in that ligure, the electrical impedance is given by where a L, is the change in L, per unit of displacement Q2, y is the ratio of mutual in'- ductance of L, and L0 to L0, and Zm is the mechanical impedance of the system.

ylhis drawing shows a magnet M with two windings on its pole the mass L2 so placed that the pull of the magnet is opposed by the spring C2. One winding of the magnet is connected to a source of direct current in series with a large inductance W which serves to keep the current n constant. The other winding is connected to a source of alternating voltage E with the condenser G1 in series.

TWe can derive the electrical impedance of this system by the use of Lagranges equation of motion which is shown below slightly CII modified to include an outside force not accounted for in T and V.

mit @v dt (at) 5g a@ (l) Here T is the kinetic energy, V is the potenv tial energy, g is the coordinate With respect d to which these energies are taken and z is g' dt E is the outside force M. F.) acting upon the system.

In this system the kinetic energy may be expressed as follows:

electrical system and the potential energy in the mechanical system. Thus:

Q2 fc e 2 O1 l D Q2 where Q1 is the charge of the condenser C1. Solving, We get:

llf l2 lf 9 2 V 202+ 02 202 202 (4) We may novv substitute in the Lagrange Where L0 is the inductance of the D. C. coil, L0 is the inductance of the A. C. coil, M is the mutual inductance of the two and 0 g2, al g2, 02 g2 are the factors of change of inductance d al t WLM 1 wat due to displacement7 the zs being constants. L2 is the mass of the movable rod and i2 is the Velocity of the mechanical system. o and c', are the D. C. and A. C. currents, respective` ly, as shown on the figure. If now,

L0=wLO and M=yL0 Equation (2) becomes Equation Treating g1 and l as the Variables and differentiating V and T in (il) and With regard to these, We obtain the Lagrange equation for the electrical system:

Since We are dealing With sine Waves, We

are ]ustitied in substituting yp toi' and for g, Where j l, thus:

02 g2 y'pLO l and 02 l 2 L0 are negligible sec ond order terms, therefore:

l E t1 ypL0 @1012120 (5) In order to get the potential energy of the Whole system, We must know the torce acting upon the mass L2, which is caused by the spring:

Now treating g2 and 2 as thevariables and differentiating Equations and With regard to them and substituting in Equation (l) We obtain for the mechanical system Fm z vvhich becomes, by making substitutions similar to those made above:

Now it is evident that the terin @LO-gif Which is due to the constant pull of the mag- D net Will cancel the term which is the con- 2 stant pull of the spring since the system is in equilibrium. )Ve may also drop azllozlz,

since it is of the second order. Thus We now have the simultaneous equations involving l and 2 given below:

l @L i@ +7.( L +.-)=El elle 2 1 JP o `72,01 7) l b2 (329132 @Loyzozl 0 Since we are interested in the electrical impedance of this device we solve for E/z'1 from the above equation lt is evident that the denominator of the last term is the impedance of the mechanical part and we thus see that the electrical impedance of this device is the sum of the reactance o1 the magnet coil, the series condenser and a term involving the reciprocal of the mechanical impedance. lt is thus evident that where the mechanical system is resonant the electrical system will be antiresonant and vice versa. This is to be expected from the operation of the device since when the mechanical system is vibrating violently or in resonance it will canse the maXimum back E. M. F. in the electrical system, thus causing an anti-resonant electrical condition and vice versa.

T new we have any complicated mechanical reactance it can be replaced at any one frequency by an equivalent single mass and elastance. Thus at this one frequency, the electrical reactance of the system will be ot the same form as (8) with the last term proportional to the reciprocal of the mechanical impedance. Since this process holds good for any frequency whatsoever, we may generalize and say that no matter what non-dissipative mechanical system is used, the electrical reactance will be l l Ze: QPL() t 't @ZZ/22021302 (9) The above considerations apply specifically to the device l' Fig. l and it is seen that any characteristic given to Zm will be reflected in the electrical characteristic Ze oit the device as a whole and that if the source E is replaced by a connection to a transmission line the apparent characteristics of that line will be correspondingly modiiied either as to impedance at various frequencies, delay in transmission or other properties.

Fig. 2 shows a modified form of mechanical device which is essentially a doubling ot that of Fig. l. Tt consists of two rods of magnetic material to which are attached a number of mechanically tuned reeds, the

whole being actuated by the coils shown. Each rod itself has mass M5 and is attached to the outside support through springs whose elastance is denoted by S0. The two rod arrangement obviates the effects of any mechanical jars on the electrical system since, for similar motion of the rods in the same direction, the reluctance of the magnetic path does not change and, therefore, building vibrations have no electrical eiifect. The plurality of tuned reeds gives the structure a plurality of resonant frequencies alternating with anti-resonant frequencies.

This system may be treated in the same manner as that of Fig. l and for it we shall show that 2 2 2 2 Ze=jpLAB+ Mliwhere Zm is the mechanical impedance of either of the two equal mechanical systems and LAB is the inductance oit the winding AB with the moving part clamped fast in its mean position.

Let us suppose that in this double system, each half has the same mechanical constants as the single system shown in Fig. 1. Tt, for the moment the circuit AB is open and if each mechanical systemy in the double device receives a displacement g2, the total mechanical potential energy will be twice that of the single system.

Thus:

We need not consider the last two terms as they drop out of the final result.

The total mechanical kinetic energy of the part which varies and so needs to be considered will also be twice that of the single system since the mass is double.

Thus:

2 Lgt?) 1327322 Thus 1 2 (se) T2 l 2 l L2 l2) :1-127122 Since these terms finally become the terms and representing mechanical reactance, it is evident that the mechanical impedance will be halved in the result. By a series of steps identical to those for the simple form, we shall have for the electrical impedance of the double system.

Vhere Zm is the mechanical impedance of either half of the device.

Again it is evident that by connecting the points AB to a `transinissioa line or other electric circuit the characteristics of the device will, by reaction, be reiiected on the transmission line or circuit. The question of so designing the mechanical device, as to siZc of masses, strength of springs and so forth, in order to give the desired characteristic to that circuit is of importance and the method which will now be set forth constitutes an essential part of our invention.

Let us suppose, as an illustration, that it is desired to design an electo-mechanical device which shall be the equivalent of the impedances Z1 or Z2 described in our copcnding application, Serial No. 134,928 filed September 11, 1926. That application relates to a network which shall give a desired frequencydelay characteristic to a transmission line. In that application, it is shown that a tan dem series of n sections of lattice-type network of constant characteristic impedance K and zero attenuation, as shown in Fig. 3 of this application, can be replaced by a network of the form shown in Fig. t, in which the impedances Z1 and Z2 may have the form of Fig. 5 or Fig. 6 and are relatedlto each other in the manner given by Z1 slitting K (11) 2 Z2 jZlf C013 2i In thiscase, the impedance Z1 will have a number of resonant frequencies alternating with anti-resonant frequencies and Z2 will be resonant when Z1 is anti-resonant and antiresonant when Z1 is resonant.

In that copending` application, a method for designing Z1 and Z2 is given to yield the desired delay characteristic. Vile will now disclose the method we prefer for the design of the electro-mechanical device to give the equivalent of an impedance Z1 or Z2. Solving Equation (10) for Zm we get Z QPyZ/QZLABZ m ZHPLAB Where Ze equals Z1 or Z2, the impedance to be simulated.

= -jH (1212er) (1032-192) (raaf-p2) (paj- The above equation gives the mechanical reactance required. Suppose we desire that the electrical reactance be anti-resonant at the frequencies p1 p3 222 1 then the mechanical reactance will be resonant at these frequencies. The frequencies at which the mechanical reactance will be anti-resonant can be determined from the resonant points of ZG-jpLAB. Having thus found the resonant and anti-resonant frequencies of the mechanical reactance, it is now necessary to find the impedance of this reactance at these frequencies. To do this we make use of a broad theorem given and proven by Foster in an article published in The Bell System Technical Journal, April, 1924, page 259. This reactance theorem states that the most general driving-point impedance Z of a finite rcsistanceless network whose resonant frequencies (i. e., Z=0) are and whose anti-resonant frequencies (iL e., Z=w) are fo:7o/27V fazpz/Qm': f4=94/27T7 etc', is given by the equation Here H is a constant factor 0 and 0 popipg .pm lzaf 0- H may be calculated from the known value of Z at some particular frequency.

In order to cover all possible cases, p1 may sometimes equal p0 and p2n 1 may become infinite while H 292.1 12 is maintained finite. For example, if the impedance to be constructed is resonant at Zero and infinity, then we will let p0=p1=0 f and p2n 1=p2n= This is illustrated by the calculation of Z1 following. 1We do not actually use either p0 or p21, in this case but 292.11 must represent the highest resonant frequency and there must be a frequency p2n p2n.1. We can think of them as pum: oo and 292,1: +1= oo for the sake of convenience. Similarly, if the desired impedance were resonant at zero and anti-resonant at infinity we would have p0: 191:0 and 2221,: but 202 1 would be the highest resonant frequency and not infinity. Keeping the above in mind, together with the fact that resonant frequencies have odd subscripts and anti-resonant frequencies have even subscripts, it is possible to assign the proper values for p0, p1, etc., for any impedance curve. Y

In order better to see the application of this equation let us consider one of the reeds of Fig. 2 as shown in Fig. 7. Since mass and the reciprocal of elastance are analogous to inductance and capacity, we are justified in saying that the reed must be either an anti-resonant or a resonant device. If we consider this rod to be actuated by an alternating force of frequency slightly greater than zero, it is evident that the effect of the reed Will be entirely due to the mass because the spring Will remain stiff. 'fhe mass will, by its inertia, give a small positive reactance to the system. As the frequency increases, this positive reactance' increases. However, if We consider a very high frequency it will be seen that the mass Will tend to stand still With the spring taking up the motion of the rod. Thus, at high frequencies the reactance is negative (due to elastance) and will become less as the frequency increases. But this is what happens in an anti-resonant electrical circuit as shown by the reactance curve of such a circuit in Fig. 8. The reed cannot be resonant because if it Were, it Would have to have innite negative reactance at zero frequency and infinite positive reactance at infinite frequency. lt must, therefore, be analogous to an anti-resonant circuit. 1n Fig. 2 there are four such anti-resonant mechanical devices in series. Also the mass M5 and spring S0 are in series with the antiresonant devices. rfaking account of the inductance LAB the structure may be represented electrically by the arrangement of coils and condensers shown in Fig. 10. It is thus evident that F osterie theoren'i applies to the mechanical impedance and can be used in the same vvay as if We Were considering a series of anti-resonant electrical circuits. For the actual constants of this mechanical system We make use of the relation derived by Foster from Equation (12) 1 jr 0- Lkpk2-Zm(pk2 p2) Where p pk (13) and Where Ck is the reciprocal of the elastance and Lk is the mass for the 70th tuned reed. lt should be noted that the subscript le is not the same as on Fig. 2, since /c is always even for anti-resonant devices (see Fig. 6).

The equation shown above gives the values for the tuned reeds in terms of the constant H (see Equation (12)). This constant may be determined from a knowledge of the reactance desired at some particular frequency.

1n all, there are four different conditions which may have to be met by the mechanical device. They are: (a) The electrical impedance of the device may be required to be Zero at zero frequency and Zero at infinite frequency, or zero at Zero frequency and infinite at infinite frequency, or (c) inlinite at both zero and infinite frequencies, or (d) infinite atzero frequency and Zero at infinite frequency. It Will be evident that the device as shown in Fig. 2 has Zero impedance at 1 Ze JPG/1B (10a) TWe may solve this equation for Zm since all the other values in the equation are knovvn. Then the masses and springs of Zm may be computed by Fosters theorem as explained above. lf ive Wish the device to have infinite reactance at Zero frequency this can be accomplished by putting a condenser in series. 1t is evident that Zm can be calculated for any combination such as this Where condensers are used either in series or in parallel. We must, of course, know What impedance is desired at Zero and infinite frequencies before We can put in the condensers and solve for Zm.

The application of this method of design and the results arising from the invention will be more clearly illustrated by a concrete problem. Let this problem consist of the design of the electro-mechanical device of Fig. 2 to be the equivalent of the impedance Z1 of Fig. l, Which is to have Zero impedance at zero frequency and at infinite frequency.

It Will be noted that a factor 107 has been introduced to reduce the electrical measurements, which are ordinarily made With the practical units, to absolute units (1 Joule :107 ergs). TWith this adjustment, the results for masses will be in grams and for elastance in dynes per centimeter.

lt is necessary to choose suitable values for LAB, CAB, a, y, o and knowing Z1, from the characteristics of the circuit to be replaced, the impedance Zm may be computed.

ln order to-design the elements of Zm it is only necessary to know the frequencies at which Zm becomes Zero and infinite and the value of Zm at some intermediate frequency, in order to determine the constant H of Equation (12).

In order to obtain satisfactory results, rcasonable assumptions must be made. Letus take LAB :.2 henry o :.1 amperes UAB F. a :.905 3/ 85 |`70 600 ohms 4 if it is desired to vary one of these factors Without changing Zm one or more of the other factors may be adjusted so that the product remains constant.

Z1, which We are to replace, is one of two impedances with the hybrid coil arrangement of Fig. 4 which was designed to replace a tandem series of six sections of lattice net- Work of the type shown in Fig. 3 and as described in our copending application referred to above. These six sections had a delay characteristic shown by curvev ci? 1i`ig. 9. In order to simulate this delay, it deve.- oped that Z1 should have a value given by Z1/j2i:tan g as curve c of F ig. 9. It will be observed that the frequencies at Which Z1 should be resoand this relation is plotted zm: H

which VZm is infinite, equate the denominator of (14) to zero, whence,

Z 'PLAB 1 j 1:2920ABLAB am /a: @LAB (1e) 2K'- p22KOABLAB Again (16) is plotted on Fig. 9 as curve e and its intersections with curve c give the frequencies at which such anti-resonance occurs as f6 :1157 f8 :1405 f10:2105 7612= OO 1412162 z Za :122)

where 29:29], and 74:0, 2, 4

nant and anti-resonant are clearly shown and thus curve c must be used in our present problem.

In order to determine the frequencies cor- 1 (14) to Zero, whence, for these frequencies:

Inserting the values of K and CAB, (15) is plotted on Fig. 9 as curve CZ. Its intersections vvith curve c give the frequencies at which such resonance occurs, as

f1 540 f, 83e f, :i006 f, :i210 f, :i471 1:2515

In order to determine the frequencies cor- L 1 responding to p2, p1, p5

292m at which the mechanical part is anti-resonant, that is, at

P(Z?22'292) (2942-202) @k2-P2) @mwa-p2) (12) The expression (13) contains a term @:Pkl (Pk2"p2) which will cancel the saine term in (12),

when (13) is substituted in (12) and thus keeps the expression determinate. The value of Ck is then obtained directly and Lk is obtained from Ck. The values obtained for the particular problem under discussion are as ollovvs:

Springs, centimeters Masses, per dyne in grains o, :0.0798 i0-7 G2 :0.407 i017 L2 :1.022 C4 :0.456 i07 L, :0.607 CG :0.367 107 LC :0.516 CS :0.260 X10'7 LS :0.494 C10: 0.0341 i0-7 L10: 1.077

In terms of the symbols used in F ig. 2,

C0:S0; L12:M5; and C12 and L0 are not present.

The springs S1, S2, S3, etc., are just twice the value of C2, C1, C6, etc., While the masses M1, M2, M3, etc. are just 1/2 the value of L2,

,1, LG, etc., since they occur in pairs.

In obtaining these results, certain boundary conditions are helpful. Since the device is to have zero impedance at zero and at in inite frequency, it is evident that C1220 and L0: i. e., these two elements are not present. From Equation (l2), taken at p: ce, it appears that L12=ll=5 grams. Also from Equation (l2) taken at 29:0, it appears that Hpl2p32 @2 12 From the value oi? C0, it is seen that the spring SO is a very still one for a` force of l0G dynes (about 2 pounds) will stretch it only 1O .O798 107=.00798 cm. lt this is too still to make easily the mechanical impedance may then be lowered. That is, multiply all Cs by a desired factor and divide all Ls by the same liactor. lf the electrical impedance is to remain unchanged, it is necessary to also lower a2 y2 o2 by the same factor as eX- plained above.

For example, let the impedance of the mechanical system be reduced to l/lO. rl`hen we change the decimal points in the results as given above, so that all springs are ten times as movable and masses are l/lO previous values. ln order to keep 'the electrical impedance the same, we must reduce a2 y2 2702 to l/lO which may be accomplisl'ied, for example, by taking which is the reciprocal ot curve c of Fig. 9, would be used. Because ot the boundary conditions CAB would be connected in series and not in parallel. As a result, the complex structures Z1 and Z2, which have been originally planned as wholly electrical, can be replaced by devices which are mainly mechanical, with the attendant advantages.

While, in this specilication, a special application of the invention has been illustrated in connection with the delay circuit of Fig. l, it is to be understood that it is 'for illustrative purposes only and is not limited to such applications. For this reason, it is to be understood also that various modifications can be made in the structure ot 2, whether it is to be used in this type o?? delay circuit or tor other purposes, without departing from the spirit of our invention.

llilhat is claimed is:

l. ln a wave delay structure an electra mechanical device comprising tuned inechanical parts associated with an electric circuit, the mechanical parts being so designed as to dimensions that the device reacts by reflection on the electric circuit in accordance with and to give a desired delay-ire quency characteristic. Y

2. in electro-mechanical device compris ing a plurality of tuned mechanical parts, a winding associated with said mechanical parts and means for connecting said winding to an electric circuit, the mechanical parts being so designed as to dimensions that the device reacts by reflection on the electric circuit to give a desired non-dissipative impedance and delay characteristic thereto.

3. An electro-mechanical device comprising a plurality of tuned mechanical parts, a

Winding associated with said mechanical parts and means 'for connecting said device to an electric circuit, the tuned mechanical parts being so designed as to frequency that the device reacts by reflection on the electric circuit in accordance with and to give a desired delay-frequency characteristic.

4. in electro-mechanical device adapted to serve as a substitute lor an electrical delay network, said device comprising a plurality ot tuned mechanical parts so designed as 'to dimensions that the said parts react by relection to give a delay characteristic equivalent to that of the network to be replaced.

5. [in electro-mechanical device designed to simulate a nonedissipative electrical delay network oi given characteristics with rescnant and anti-resonant frequencies, said device comprising vibratory mechanical niembers tuned to frequencies determined by the resonant and anti-resonant frequencies oit the network to be simulated.

6. An electro-mechanical device designee to simulate a non-dissipative electrical delay network of given characteristics, said device comprising vibratory mechanical members and a winding associated with said inembers, the dimensions of the winding and the frequency oi' the members being so designed as to give by reflection a non-dissipative eelay characteristic to the device equivalent to that of the network to be simulated.

7. An electro-mechanical device designed to simulate an electrical network of given characteristics and consisting of a plura ity of parallel branches oi' series inductance and capacity with resonant and anti-resonant lirequencies, said device comprising a winding` with a movable magnetic core, a support, a spring attaching the core to the srq port, a plurality of similar vibratory elements attached to the core, the core and spring and the vibratory elements being tuned to frequencies determined by the resonant and ISO anti-resonant frequencies of the network to be simulated.

8. An electro-mechanical device designe-:l to simulate an electrical network of given delay characteristics with resonant and anti-resonant frequencies, said device comprising a winding and a plurality of tuned mechanical parts, each of said tuned mechanical parts comprising a spring member and a mass, each of said parts being` tuned to a frequency determined by the resonant and anti-resonant frequencies of the network to be simulated.

9. In a transmission line, a delay correction network comprisine a hybrid coil and two non-dissipative impedances associated therewith, the said impedances being` mainly mechanical, the parts beingso designed as to react on the electrical circuit to give the desired delay characteristic.

10. In a delay transducer' of a predetermined delay-frequency characteristic, a composite electrical. and mechanical device comprising electrical elements and mechanical elements, means for impressing a complex electrical wave on the electrical part, the mechanical part being` designed to convert the electrical wave into a mechanical wave, to transmit this wave and reflect it back vinto the electrical part with a delay for each component of the wave to yield an overall delay equal to the predetermined delay-frequency characteristic.

11. A phase delay compensator adapted to be associated with a transmission line comprising a transformer and a complex impedance, said impedance comprising electrical elements and mechanical elements and having resonant and anti-resonant frequencies,

` the constants of the impedance having values which bear a definite relation'to the delay of an equivalent lattice net-work at each resonant and anti-resonant frequency.

12. In a delay transducer of a predetermined delay-frequency characteristic, a composite electrical and mechanical device coinprising electrical elements and mechanical elements, means for impressing a complex wave on the electrical part, the n'iechanical part being so designed that the impedance of the composite device is equal to the electrical impedance plus a multiple of the reciprocal of the mechanical impedance.

13. An electro-mechanical device designed to simulate an electrical network of given characteristics and having resonant and antiresonant frequencies, said device comprising a winding` with a movable magnetic core, a support, a spring attachingl the core to the support, and a plurality of similar vibratory elements attached to the core, the core and spring and the vibratory elements being,` anti- 1 resonant and resonant at approximately the In testimony whereof, we have signed our' names to this specification this 10th day of September 1926.

HARRY NYQUIST. KENNETH W. PFLEGER. 

